# Category Using gret l for Principles of Econometrics, 4th Edition

## Multinomial Logit

Starting with version 1.8.1, Gretl includes a routine to estimate multinomial logit (MNL) using maximum likelihood. In versions before 1.8.1 the alternatives were either (1) use gretl’s maximum likelihood module to estimate your own or (2) use another piece of software! In this section we’ll estimate the multinomial logit model using the native gretl function and I’ll relegate the other methods to a separate (optional) section 16.3.1. The other methods serve as good examples of how to use gretl’s scripting language and how to use it in conjunction with R.

In this model the dependent variable is categorical and is coded in the following way...

## VECM: Australian and U. S. GDP

You have two difference stationary series that are cointegrated. Consequently, an error cor­rection model of the short-run dynamics can be estimated using least squares. A simple error

and the estimates

AaUst = 0.491706+—0.0987029et_ 1

(8.491) (-2.077)

Ausat = 0.509884 ++0.0302501et_ 1

(10.924) (0.790)

(t-statistics in parentheses)

which are produced using

1 ols diff(aus) const uhat(-1)

2 ols diff(usa) const uhat(-1)

The significant negative coefficient on et-1 indicates that Australian GDP responds to a temporary disequilibrium between the U. S. and Australia.

The U. S. does not appear to respond to a disequilibrium between the two economies; the t-ratio on et-1 is insignificant. These results support the idea that economic conditions in Australia depend on those in the U. S...

## Using R with gretl

Another feature of gretl that makes it extremely powerful is its ability to work with another free program called R. R is actually a programming language for which many statistical procedures have been written. Although gretl is powerful, there are still many things that it won’t do, at least without some additional programming. The ability to export gretl data into R makes it possible to do some sophisticated analysis with relative ease.

Quoting from the R web site

R is a system for statistical computation and graphics. It consists of a language plus a run-time environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files.

The design of R has been heavily influenced by two existing languages: Becker, Cham­bers & Wilks’ ...

## Testing for Weak Instruments

To test for weak instruments, regress each independent variable suspected of being contempora­neously correlated with the error (xk) onto all of the instruments (internal and external). Suppose xK is the endogenous regressor. The first stage regression is:

xk = Yi + Y2X2 +—– + Y к-1XK-1 + вігі +——- + Olzl + vk (10.5)

In this notation, the z1, …, zl are the external instruments. The others, x2, …, zk-1 are exogenous and are used as instruments for themselves (i. e., internal to the model). If the F – statistic associated with the hypothesis that the coefficients on the external instruments, в1, …, eL are jointly zero is less than 10, then you conclude that the instruments are weak. If it is greater than 10, you conclude that the instruments are strong enough...

## Fixed Effects

The model (15.2) is reestimated using fixed effects. Race and education do not change for individuals in the sample, and their influences cannot be estimated using fixed effects.

1 open "c:Program Filesgretldatapoenels_panel. gdt"

2 list xvars = const educ exper exper2 tenure tenure2 south union black

3 panel lwage xvars —fixed-effects

4

4 xvars -= educ black

5 panel lwage xvars —fixed-effects

Even though the parameters for black and educ are not identified in this model, we included them anyway in line 3 just to see how gretl handles this. The results are:

Fixed-effects, using 3580 observations
Included 716 cross-sectional units

Time-series length = 5
Dependent variable: lwage

 Coefficient Std. Error t-ratio p-value const 1.45003 0.0401400 36.1244 0.0000 exper